Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity

In this paper, we study a joint optimization problem of replenishment and pricing for a periodic-review inventory system with random supply capacity. When making replenishment and pricing decisions at the beginning of each period, the firm only knows the supplier’s available capacity in the current period, but does not know what will be the available capacity in future periods. The salient feature of our model is that the random supply capacities for different periods are dependent. Several stochastic dependency structures are considered for the supply capacity sequence, including the one-lag and the multi-lag dependency.We show that the optimal inventory control policy is of the modified base-stock type and the base-stock level is decreasing in the available capacity of the current period and that the optimal pricing policy is a “list-price” coined with markdown and markup. This paper generalizes the work of Federgruen and Zipkin [Federgruen, A., Zipkin, P., 1986a. An inventory model with limited production capacity and uncertain demands I. The average cost criterion. Mathematics of Operations Research 11, 193–207; Federgruen, A., Zipkin, P., 1986b. An inventory model with limited production capacity and uncertain demands II. The discounted cost criterion. Mathematics of Operations Research 11, 208–215] in which the supply capacity and selling price are assumed to be fixed constants, and the work of Federgruen and Heching [Federgruen, A., Heching, A., 1999. Combining pricing and inventory control under uncertainty. Operations Research, 47, 454–475] on joint optimization of replenishment and pricing with unlimited supply capacity.